Hitherto, two fundamentally different processes are known for translating the sampling rate of a sampled signal.
The first process consists of converting the sampled quantized signal into a continuous signal. An analog low-pass filter suppresses the high frequency portions of the input signal. The continuous signal brought about by the conversion is then sampled again at the desired output-side sampling rate. Band limitations which may be necessary for preventing aliasing is obtained by a corresponding dimensioning of the low-pass filter. In working with sampled signals in digital form, this process required the use of a digital-analog converter and an analog-digital converter, which involves high costs.
This process for translating the sampling rate is nowhere explicitly described in the literature but can be attributed to the prior art.
In the case of sampled signals, there is fundamentally a second process for translating the sampling rate, but only if there is a fixed relationship between the input and output sampling rates. If the relationship between the two sampling rates is represented as the relationship between two integers, then the two sampling rates have joint integral multiple rates. The sampling rate is translated by increasing the input sampling rate to one of the joint integral multiple rates and by subsequent reduction to the output sampling rate, both in an integral ratio. To increase the sampling rate by a factor N, initially in each case (N-1) equidistant, zero-value sampling values are introduced between two succeeding sampling values of the input sampling sequence. The resulting signal has the same spectrum as the original signal, but a correspondingly increased sampling rate.
For the further processing of the signal, the higher partial spectrum between the half of the original sampling rate and the half of the new, higher sampling rate must be suppressed, which is carried out with a low-pass sampling filter. By undersampling the new sampling sequence with the output sampling rate, the spectrum is aliased. A band limitation which may be required for preventing aliasing can be achieved by corresponding dimensioning of the low-pass sampling filter.
The significance of this is related to a sampling therorem generally known in the art. This theorem holds that an audio signal of, e.g., 20 kHz bandwidth has to be sampled at least 40,000 times per second, or the original signal will not be recovertable from the samples. Technically, the sampling theorem has one important consequence. If signals are still present anywhere beyond half the sampling frequency, sampling will modulate them back into the signal band, a phenomenon described as "aliasing". Therefore, the analog input signal has to be cleaned from any signal with a frequency higher than half the sampling frequency.
If transverse filters are used for low-pass filtering, a considerable part of the processing expenditure can be avoided by not carrying out those multiplications of signal variables with filter coefficients in which the variables have a zero value and there is no need to determine the intermediate values of the sampling sequence with the higher sampling rate, which are not required due to the undersampling.
The sampling rates at the input and output determine the smallest possible integral multiple rate, as well as the coefficients of the sampling filter, which must therefore be redimensioned for every new relationship or ratio of the two sampling rates. This type of sampling rate translation is described, e.g., in Schaefer & Rabiner, A Digital Signal Processing Approach to Interpolation, Proc. IEEE, pp. 692-702, Vol. 61, No. 6, June 1973.
A disadvantage of the latter process is that when simple relationships between the input and output sampling rates do not exist, the smallest joint integral multiple rate will be very high. This requires a correspondingly high filter order, because the relative steepness of the amplitude response of the low-pass sampling filter consequently increases.
An increase or decrease in the sampling rate can also take place in a number of stages. It is advantageous in this connection that the individual filter orders can be made lower.